Homology of Fibrations

Abstract

AbstractIn 1935, at the instigation of Hopf, his student Stiefel undertook in his dissertation [457] to extend Hopf’s work on vector fields (Part 2, chap. Ill, §3). Given an n-dimensional compact C∞ manifold M, the problem was to investigate whether there exists on M, not only one nowhere vanishing vector field, but a system of m vector fieldsX j (1≤j≤m) for some m≤n, subject to the condition that at each point x ∈ M, the m tangent vectors X j(x) are linearly independent (hence≠0). The case m = n is particularly interesting in differential geometry, because the existence of such systems of n vector fields is equivalent to the existence of a parallelism on M.KeywordsVector FieldDifferential GeometryTangent VectorAlgebraic TopologyDifferential TopologyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.